All DFTB calculations discussed within this work were performed with the DFTB+ code[1]}, [2]}, using self-consistent charges (SCC)[3]} and charge convergence criteria of \(2.72 \times 10^{-5}\)  eV (\(10^{-6}\)  au). Inclusion of an external van der Waals correction[4]}, [5]} is beyond the scope of our present study. We have performed “shell-resolved” SCC calculations, where separate Hubbard \(U\)  parameters were determined for each orbital angular momentum shell. Hubbard \(U\)  derivatives were computed numerically for blackDFTB3-dens calculations, where we determined values of \(-0.0328\) , \(-0.0840\) , and \(-0.05334\)  for the \(s\) , \(p\) , and \(d\) -orbital interactions for Ti and a value of \(-0.1857\)  for the \(s\) -orbital for H. We have also applied an exponential charge damping factor for Ti-H interactions of 3.5, similar to previous efforts[6]}. The properties investigated here were largely insensitive to choice of either Hubbard \(U\)  derivative or damping factor values. The same electron thermal smearing and k-point mesh were used as described for our DFT calculations for each system.
